CN104158787B - Based on the nonlinear impairments compensation method of VOLTERRA model in OFDM-PON system - Google Patents

Abstract

The invention proposes a nonlinear damage compensation method based on a VOLTERRA model in an OFDM-PON system. (1), store the same sequence in the database at the transmitting end and the receiving end respectively; (2), send information with pilot sequence and extract it at the receiving end; (3), construct according to the characteristics of the model matrix; (4), construct the VOLTERRA model matrix form; (5), solve the initial value of the identification vector; (6), analyze the constellation diagram to construct the difference factor vector; (7), and continuously construct new weight vectors. This method uses the VOLTERRA model to identify various nonlinear damages in the OFDM-PON system, uses the dimension of the QR decomposition matrix to reduce the complexity of the solution, and performs adaptive correction processing on the identification coefficient vector, which improves the system's ability to resist nonlinear interference and reliability .

Description

Nonlinear Damage Compensation Method Based on VOLTERRA Model in OFDM-PON System

technical field

The present invention relates to a method in the technical field of next-generation access system compensation, in particular to an Orthogonal Frequency Division Multiplexing-Passive Optical Networks (OFDM-PON) system based on the VOLTERRA model non-linear compensation method.

Background technique

The reliability and anti-interference ability of OFDM-PON system can be improved by using the nonlinear damage compensation method based on VOLTERRA model on the receiver.

The existing nonlinear damage compensation methods are mainly aimed at nonlinear effects such as phase noise, cross-phase modulation, self-phase modulation, four-wave mixing, and additive non-Gaussian noise in optical fiber communication systems. The existing research programs mainly focus on Optical OFDM (Optical OFDM, O-OFDM) system. The existing nonlinear compensation algorithm based on the pilot sequence is as follows: a pre-designed same sequence is stored at the transmitting end and the receiving end, and the receiving end uses the training sequence to obtain and store the basic channel state information (Channel State Information, CSI). After the information with the preset sequence sent by the sending end reaches the receiving end, it first passes through the self-phase modulation compensator module, and then extracts the information at a specific position and multiplies it with the preset sequence stored at the receiving end, and selects the corresponding result for use in Phase Noise Compensation. The disadvantage of this method is that it needs to rely on the self-phase modulation compensation module to better realize the phase compensation process; the compensation method based on digital pre-distortion (Digital Pre-Distortion, DPD) is: deploy the same DPD module at the transmitter and receiver, The DPD output at the receiving end is compared with the DPD output at the transmitting end, and the comparison result is used as one of the input signals of the DPD at the receiving end. The DPD module uses polynomial functions to approximate the nonlinear effects of O-OFDM systems and relies on sensitive, high-speed photodetectors and analog-to-digital converters. The disadvantage of this method is that it requires high equipment cost in the actual deployment process; the compensation method based on the VOLTERRA model is: store the same sequence at the transmitting end and the receiving end, and after the transmitting end sends the sequence, use VOLTERRA at the receiving end to The series decomposes the received sequence, and the basis vector of the series is formed by the sequence stored at the receiving end. Afterwards, the coefficient vector of the basis vector can be solved to realize the establishment of the VOLT-ERRA model, and further realize the identification of the O-OFDM system according to the model. The disadvantage of this method is that the coefficient vector cannot be adjusted adaptively, and the calculation of the coefficient vector requires a large amount of calculation, which deteriorates the computational efficiency of the system. In addition, the above three methods only realize the nonlinear compensation for the O-OFDM system, without further analysis for the OFDM-PON system.

Contents of the invention

The purpose of the present invention is to address the deficiencies in the prior art, and propose a nonlinear damage compensation method based on the VOLTERRA model in the OFDM-PON system, so as to solve the problem that the existing compensation method cannot effectively deal with the OFDM-PON system and the compensation method has high complexity, The problem of low performance and adaptive coefficient adjustment can improve the reliability and anti-interference ability of the system.

In order to achieve the above object, the idea of the present invention is: implement a compensator based on the VOLTERRA model in the digital signal processing (Digital Signal Processing, DSP) module of the receiving end of the OFDM-PON system, and construct a non- The linear identification scheme maps the infinite base coefficients to the finite coefficient vectors to realize the solution of the VOLTERRA nonlinear identification model and the compensation of the nonlinear influence of the system.

According to the above inventive concepts, the present invention is realized through the following technical solutions.

A nonlinear damage compensation method based on the VOLTERRA model in an OFDM-PON system, characterized in that the specific operation steps are as follows:

Step 1. Store the same sequence: store the same sequence in the database at the transmitting end and the receiving end respectively;

Step 2. Send information with pilot sequences: the transmitter extracts part of the sequence from the database as a pilot sequence and intersperses it with useful information and sends it to the receiver. The receiver receives and extracts the pilot information that has experienced nonlinear damage. ;

Step three, build Matrix: The extracted information is constructed using the KRONECKER product according to the characteristics of the third-order VOLTERRA model matrix;

Step 4. Construct VOLTERRA model matrix form: use The corresponding sequence extracted from the matrix and the receiving end database is obtained to obtain the matrix form of the VOLTERRA model for identifying the nonlinear damage of the OFDM-PON system;

Step 5. Solve the initial value of the identification vector: perform QR decomposition on the matrix model obtained in step 4 to obtain the initial value of the identification coefficient vector;

Step 6. Build a difference factor vector: analyze the 16QAM constellation diagram after the non-pilot sequence of the received information passes through the VOLTERRA compensator, and use the difference between the standard constellation point and the non-ideal constellation point to construct the difference factor vector;

Step 7. Construct the weight vector: use the vector obtained in step 6 to update the newly obtained information value of the identification coefficient vector, and use this information as a weight vector for correcting the sequence at the current non-pilot position.

The specific operation method for storing the same sequence described in the above step 1 is as follows: store the same sequence in the database at the transmitting end and the receiving end respectively, and use the sequence as a pilot at the transmitting end, where the pilot refers to interspersed in the sequence according to a given rule Sequence between useful information sequences; use vector Indicates the transmitted pilot information, vector Represents the received information experiencing nonlinear damage, where , , representation vector Elements, is the number of pilot subcarriers, represents the transpose operation, representation vector Elements.

The specific operation method of sending the information with the pilot sequence described in the above step 2 is as follows: the method of given interleaving refers to the method of comb insertion, and the useful information is any information for reaching the purpose of communication. express; will Insert the comb into the Get the information with the vector Representation; at the receiving end with Corresponding information vector represent, with the vector Corresponding information vector express; among them , , , ; , , and represent vectors respectively , , and Elements, Indicates the number of useful information subcarriers, represents the total number of subcarriers, and ; The nonlinear damage refers to various nonlinear effects in the OFDM-PON system including phase noise, cross-phase modulation, self-phase modulation, four-wave mixing and additive non-Gaussian noise.

Build as described in Step 3 above The specific operation method of the matrix is as follows: Using the VOLTERRA model, it is assumed that the vector received by the receiving end The vector obtained after the VOLTERRA compensator is denoted as ,in . So there is

(1)

Among them, the vector is the output of the compensator, represent the elements of this vector, , Error vector for the VOLTERRA model First elements, In order to identify the first OFDM-PON system model order identification coefficient, and the function composed of this coefficient is called the generalized inverse function of the channel function;

Write formula (1) in matrix form, we have

(2)

Among them, the matrix , express set of complex real numbers of dimension, vector It is completely obtained by the identification coefficient through elementary matrix transformation, ; representation matrix First A row vector of row elements, expressed as

(3)

in, , is the maximum order taken by the VOLTERRA model, is the memory length of the OFDM-PON system; the visible matrix The number of dimension entirely by and Sure, ; in general, there is always ; (3) in the formula Indicates KRONECKER product. represents the transposed row vector The resulting column vector.

The specific operation method for constructing the matrix form of the VOLTERRA model described in the above step 4 is as follows: the sequence extracted from the receiving end database is and Exactly the same information, the sequence is the VOLTERRA model output signal ideal value of ,or

(4)

Among them, the vector for sequence with sequence Between the error vectors, the part of the (4) error sequence is combined, that is, ,Have

(5)

Equation (5) is the VOLTERRA model matrix form of the nonlinear influence.

The specific operation method for solving the initial value of the identification vector described in the above step five is as follows: the process of solving the identification coefficient vector is:

①, pair matrix QR decomposition, with , where the matrix is an orthogonal matrix, is an upper triangular matrix, and ;

②, use matrix Transform (5), we have , so as to get

(6)

in, , Represents a vector before elements form a new column vector;

③. Use the backward iterative method to solve the vector in (6) The value of is the initial value of the identification coefficient vector, denoted as .

The specific operation method of constructing the difference factor vector described in the above step six is as follows: the QAM constellation diagram is a quadrature amplitude modulation diagram, and the pilot vector The first useful information vector after recorded as , experience nonlinear effects and reach the receiving end, so the received signal recorded as ,Depend on Get the corresponding upper triangular matrix , then use the VOLTERRA compensator for the Compensation, where the coefficient vector of the compensator is the initial value of the identification coefficient vector obtained in step five , and the corresponding VOLTERRA compensator output is denoted as ,in ;analyze The 16QAM constellation diagram, compare the constellation diagram with the standard constellation diagram, and use a series of ratios between standard constellation points and non-ideal constellation points to form a vector , which is the difference factor vector.

The specific operation method of constructing the weight vector described in the above-mentioned step seven is as follows: the latest identification coefficient vector information is obtained according to the following process:

Use difference factor vector A further correction is made to the output of the compensator, namely

(7)

in, Product for HADAMARD, is to receive the signal Compensation results;

Ruoji ,in make established, so (7) can be written as ; and will Compared with the standard constellation diagram, press Solve method to get , so that the received signal The output signal after passing through the VOLTERRA compensator can be written as

(8)

in That is, the updated identification coefficient vector information value; thus, the first receive signal The output signal after passing through the VOLTERRA compensator can be written as

(9)

Compared with the prior art, the nonlinear compensation method based on VOLTERRA model adaptive correction in the OFDM-PON system of the present invention has the following advantages: use the VOLTERRA model to identify various nonlinear effects in the OFDM-PON system, use the QR decomposition matrix dimension The number reduces the complexity of the solution, and the identification coefficient vector is adaptively corrected, which improves the system's ability to resist nonlinear interference and reliability.

Description of drawings

FIG. 1 is a schematic diagram of an OFDM-PON optical fiber communication system.

Figure 2 is a flowchart of the implementation of the compensation method.

Fig. 3 is a diagram of the self-adaptive correction process of the identification coefficient vector.

Figure 4 is a constellation diagram with non-ideal points.

Figure 5 is the result of the system bit error rate varying with the bit rate.

Detailed ways

The preferred embodiments of the present invention will be described in further detail below in conjunction with the accompanying drawings.

This example is implemented on the premise of the technical solution of the present invention, and detailed implementation, operation process and experimental results are given, but the protection scope of the present invention is not limited to the following examples.

Embodiment one:

Referring to Figures 1-5, the nonlinear damage compensation method based on the VOLTERRA model in this OFDM-PON system.

Embodiment two:

Referring to Figure 1-Figure 5, the nonlinear damage compensation method based on the VOLTERRA model in the OFDM-PON system: the system of this method consists of an optical network unit, an optical transmission channel, an optical distribution network, an optical line terminal, and a DSP module, as shown in Figure 1 Show. The optical network unit includes an electrical domain modulation module and an electro-optical conversion module, the optical line terminal includes a photoelectric conversion module and an electrical domain demodulation module, and the nonlinear damage compensator based on the VOLTERRRA model is implemented in the DSP module. The specific steps are as follows, as shown in Figure 2:

Step 1. Store the same sequence in the database at the transmitting end and the receiving end respectively, and use the sequence at the transmitting end as a pilot, where the pilot refers to a sequence interspersed between useful information sequences according to a given rule; use the vector Indicates the transmitted pilot information, vector Represents the received information experiencing nonlinear damage, where , , representation vector Elements, is the number of pilot subcarriers, represents the transpose operation, representation vector Elements;

Step 2, use the comb insertion method at the transmitter to insert the pilot sequence Insert into useful information sequence by comb Get the information with the vector express; in During the transmission process, it will be affected by various nonlinear impairments including phase noise, cross-phase modulation, self-phase modulation and four-wave mixing, and additive non-Gaussian noise. Receiver and Corresponding information vector represent, with the vector Corresponding information vector express; among them , , , ; , , and represent vectors respectively , , and Elements, Indicates the number of useful information subcarriers, represents the total number of subcarriers, and ;

Step 3. Using the VOLTERRA model, assume that the vector received by the receiving end After passing through the VOLTERRA compensator, the vector is obtained ,in . So there is

(1)

in , Error vector for the VOLTERRA model First elements, In order to identify the first OFDM-PON system model The order identification coefficient, and the function composed of this coefficient is called the generalized inverse function of the channel function.

Write formula (1) in matrix form, we have

(2)

Among them, the matrix , ,vector It is completely obtained by the identification coefficient through elementary matrix transformation. representation matrix First row elements, expressed as

(3)

Among them, the vector is the output of the compensator, represent the elements of this vector, , Error vector for the VOLTERRA model First elements, In order to identify the first OFDM-PON system model The order identification coefficient, and the function composed of this coefficient is called the generalized inverse function of the channel function.

Write formula (1) in matrix form, we have

(2)

Among them, the matrix , express set of complex real numbers of dimension, vector It is completely obtained by the identification coefficient through elementary matrix transformation, . representation matrix First A row vector of row elements, expressed as

(3)

in, , is the maximum order taken by the VOLTERRA model, is the memory length of the OFDM-PON system. visible matrix The number of dimension entirely by and Sure, ; in general, there is always ; (3) in the formula Indicates KRONECKER product. represents the transposed row vector The resulting column vector.

Step 4, the sequence extracted from the receiving end database is Exactly the same information, the sequence is the VOLTERRA model output signal ideal value of ,or

(4)

Among them, the vector for sequence with sequence Between the error vectors, the part of the (4) error sequence is combined, that is, ,Have

(5)

Equation (5) is the VOLTERRA model matrix form of the nonlinear influence.

Step 5. Obtain the identification coefficient vector according to the following process, as shown in Figure 3:

①, pair matrix QR decomposition, with , where the matrix is an orthogonal matrix, is an upper triangular matrix, and ;

②, use matrix Transform (5), we have , so as to get

(6)

in, , Represents a vector before elements to form a new vector;

③. Use the backward iterative method to solve the vector in (6) The value of is the initial value of the identification coefficient vector, denoted as .

Step 6. Analyze the 16QAM constellation diagram after the non-pilot sequence of the received information passes through the VOLTERRA compensator, and record the pilot vector The first useful information vector after recorded as , experience nonlinear effects and reach the receiving end, so the received signal recorded as ,Depend on Get the corresponding upper triangular matrix , then use the VOLTERRA compensator for the Compensation, where the coefficient vector of the compensator is the initial value of the identification coefficient vector obtained in step five , and the corresponding VOLTERRA compensator output is denoted as ,in ;analyze 16QAM constellation diagram, compare the constellation diagram with the standard constellation diagram, as shown in Figure 4, use a series of ratios of standard constellation points and non-ideal constellation points to form a vector , which is the difference factor vector, its elements The value of is determined by the ratio of the coordinate values of standard point A and non-ideal point B.

Step 7. Use the difference factor vector A further correction is made to the output of the compensator, namely

(7)

in, Product for HADAMARD, is to receive the signal Compensation results;

Ruoji ,in make established, so (7) can be written as ; and will Compared with the standard constellation diagram, press Solve method to get , so that the received signal The output signal after passing through the VOLTERRA compensator can be written as

(8)

in That is, the updated identification coefficient vector information value; thus, the first receive signal The output signal after passing through the VOLTERRA compensator can be written as

(9)

Update the identification coefficient vector value according to the above iterative method until the end of the communication process.

Fig. 5 is a graph showing the variation of the system bit error rate performance with the system bit rate when the optical fiber transmission channel length is 10KM.

It can be seen from the results of the above embodiments that the present invention can enable the OFDM-PON system to obtain higher system performance.

Claims (8)

1. A nonlinear damage compensation method based on a VOLTERRA model in an OFDM-PON system is characterized by comprising the following specific operation steps:

step one, storing the same sequence: storing the same sequence to a database at a transmitting end and a receiving end respectively;

step two, sending information with a pilot frequency sequence: the transmitting terminal extracts partial sequence from the database as pilot frequency sequence and transmits it to the receiving terminal after inserting in useful information, the receiving terminal receives the pilot frequency sequence which has undergone nonlinear damage and extracts it;

step three, constructing a K matrix: constructing a K matrix by using a KRONECKER product according to the characteristics of a three-order VOLTERRA model by using the extracted information;

step four, constructing a VOLTERRA model matrix form: obtaining a VOLTERRA model matrix form for identifying the nonlinear damage of the OFDM-PON system by using the K matrix and the corresponding sequence extracted from the receiving end database;

step five, solving the initial value of the identification coefficient vector: performing QR decomposition on the VOLTERRA model matrix form model obtained in the step four to obtain an initial value of the identification coefficient vector;

step six, constructing a difference factor vector: analyzing a 16QAM constellation diagram of a received information non-pilot frequency position sequence after the sequence passes through a VOLTERRA compensator, and constructing a difference factor vector by using the difference between a standard constellation point and a non-ideal constellation point;

step seven, constructing a weight vector: and updating the initial value of the identification coefficient vector obtained newly by using the vector obtained in the step six, and taking the information as the weight vector for correcting the current non-pilot frequency position sequence.

2. The nonlinear impairment compensation method based on the VOLTERRA model in the OFDM-PON system according to claim 1, wherein the specific operation method of the step one for storing the same sequence is as follows: storing the same sequence to a database at a transmitting end and a receiving end respectively, and taking the sequence as a pilot frequency at the transmitting end, wherein the pilot frequency is a sequence which is inserted between useful information sequences according to a given inserting method; by vector x_pIndicating the transmitted pilot sequence, vector y_pIndicating a received pilot sequence experiencing non-linear impairments, wherein

x_p＝[x_p(0),x_p(1),…,x_p(N_p-1)]^T，

y_p＝[y_p(0),y_p(1),…,y_p(N_p-1)]^T，x_pDenotes the vector x_pElement (b) of (A), N_pFor the number of pilot subcarriers, (+)^TDenotes a transposition operation, y_p(. represents vector y)_pOf (2) is used.

3. The nonlinear impairment compensation method based on the VOLTERRA model in the OFDM-PON system according to claim 2, wherein the specific operation method for sending the information with the pilot sequence is as follows: the given inserting method in the second step is a comb inserting method, the useful information is any information for achieving the purpose of communication, and the vector x is used_uRepresents; x is to be_pInserting into x in comb form_uThe obtained information is represented by a vector x; at the receiving end and x_uCorresponding information vector y_uRepresenting, information corresponding to the vector x is represented by a vector y; wherein x_u＝[x_u(0),x_u(1),…,x_u(N_u-1)]^T，

x＝[x(0),x(1),…,x(N-1)]^T，

y_u＝[y_u(0),y_u(1),…,y_u(N_u-1)]^T，

y＝[y(0),y(1),…,y(N-1)]^T；x_u(*)、x(*)、y_u(. about.) and y (. about.) denote vectors x, respectively_u、x、y_uAnd y is the element, N_uIndicating the number of useful information sub-carriers, N indicating the total number of sub-carriers, and N ═ N_p+N_u(ii) a The nonlinear damage refers to various nonlinear influences including phase noise, cross phase modulation, self phase modulation, four-wave mixing and additive non-Gaussian noise in the OFDM-PON system.

4. The nonlinear impairment compensation method based on the VOLTERRA model in the OFDM-PON system according to claim 2, wherein the specific operation method for constructing the K matrix in the third step is as follows:

using the VOLTERRA model, assume the vector y received at the receiving end_pAfter passing through the VOLTERRA compensator, a vector u is obtained, where u is [ u (0), u (1), …, u (N)_p-1)]^T(ii) a Thus, there are:

where the vector u is the output of the compensator, u (—) represents the elements of the vector, N ∈ [0, N_p-1]I ∈ [1, + ∞), e (n) is the (n +1) th element of the VOLTERRA model error vector e,identifying coefficients of the ith order of an OFDM-PON system model, and calling a function formed by the coefficients as a generalized inverse function of a channel function;

writing formula (1) in matrix form, having

u＝Kw+e (2)

Wherein, the matrix Representing a complex real number set of dimensions NxM, the vector w is obtained by elementary matrix transformation of the identification coefficients, the row vector composed of (n +1) th row elements of the matrix K is expressed as

Wherein,order is the maximum order taken by the VOLTERRA model, and L is the memory length of the OFDM-PON system; it can be seen that the column dimension M of matrix K is completely determined by order and L,generally, there is always M < N; (3) in the formulaRepresents the KRONECKER product;representing transposed row vectorsThe resulting column vector.

5. The nonlinear impairment compensation method based on a VOLTERRA model in the OFDM-PON system according to claim 4, wherein the specific operation method in the form of the VOLTERRA model matrix constructed in the fourth step is as follows:

the sequence extracted from the receiving end database is the AND vector x_pThe exact same information, the sequence being the ideal value of the output signal u of the VOLTERRA model, i.e. x_pKw + e, or

x_p＝Kw+e+e′ (4)

Wherein, the matrix Representing a complex real number set of dimension NxM, the vector w is obtained by elementary matrix transformation of the identification coefficients, and the vector e' is a sequence u and a sequence x_pThe error vector between, the error sequence part of formula (4) is merged, i.e. the orderIs provided with

(5) The formula is the VOLTERRA model matrix form of the nonlinear damage.

6. The nonlinear impairment compensation method in an OFDM-PON system based on a VOLTERRA model according to claim 5, wherein the specific operation method of solving the initial value of the identification coefficient vector in the step five is as follows:

the process of solving the initial value of the identification coefficient vector is as follows:

①, decomposing the matrix KQR, havingWherein the matrix Q is an orthogonal matrix, R is an upper triangular matrix, and

② transformation of equation (5) using matrix Q, hasThereby obtaining

Wherein,f^M(λ) represents taking the first M elements of vector λ to form a new vector;

③, solving the value of the vector w in the formula (6) by using a backward iteration method, namely the initial value of the identification coefficient vector, which is marked as w₀。

7. The nonlinear impairment compensation method based on the VOLTERRA model in the OFDM-PON system according to claim 6, wherein the specific operation method for constructing the difference factor vector in the sixth step is as follows:

the QAM constellation diagram is a quadrature amplitude modulation diagram, and the vector x is recorded_pThe first useful letter thereafterInformation vector x_uIs marked asExperiences a non-linear effect on its arrival at the receiving end, and receives the signal y_uIs marked asByObtaining an upper triangular matrix corresponding to the upper triangular matrixThen using the VOLTERRA compensator pair y_uCompensation is carried out, wherein the coefficient vector of the compensator is the initial value w of the identification coefficient vector obtained in the step five₀The corresponding VOLTERRA compensator output is noted as u₀Whereinf^M(λ) represents taking the first M elements of vector λ to form a new vector; analysis u₀Comparing the constellation diagram with a standard constellation diagram, and forming a vector v by using a series of ratios of standard constellation points and non-ideal constellation points₀I.e. the vector of disparity factors.

8. The nonlinear impairment compensation method based on the VOLTERRA model in the OFDM-PON system according to claim 7, wherein the specific operation method for constructing the weight vector in the seventh step is as follows: the initial value of the latest identification coefficient vector is obtained according to the following process:

using a disparity factor vector v₀The output of the compensator is further modified, i.e.

Wherein ⊙ is the HADAMARD product,i.e. the received signalA compensation result;f^M(λ) represents taking the first M elements of vector λ to form a new vector;

if rememberWhereinSo thatThen, the formula (7) can be written asAnd will beComparing the constellation diagram with the standard constellation diagram according to the solution v₀The method gives v₁Thereby having a received signalThe output signal after passing through the VOLTERRA compensator can be written as

WhereinIs the updated identificationIdentifying an initial value of a coefficient vector; thus, the (k +1) th received signalThe output signal after passing through the VOLTERRA compensator can be written as: